Sun Aug  9 11:36:23 2026 

einsum_test():
  R version 4.1.2 (2021-11-01) 
  einsum() carries out Einstein summation.

  matrix_column_sum_test():

  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
[3,]   31   32   33


  Ac = einsum ( 'ij -> j', A ):
[1] 63 66 69

  matrix_diagonal_test():

  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
[3,]   31   32   33

  D = einsum ( 'ii -> i', A ):
[1] 11 22 33
  matrix_matrix_multiplication_test():
  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
  B:
     [,1] [,2]
[1,]    1    2
[2,]    3    4
[3,]    5    6
  AB = einsum ( 'ij -> jk', A, B ):
     [,1] [,2]
[1,]  112  148
[2,]  202  268
  matrix_matrix_multiplication_hadamard_test():

  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23

  B:
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6

  AB = einsum ( 'ij,ij -> ij', A, B ):
     [,1] [,2] [,3]
[1,]   11   24   39
[2,]   84  110  138
  matrix_row_sum_test():
  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
[3,]   31   32   33
  Ar = einsum ( 'ij -> i', A ):
[1] 36 66 96
  matrix_trace_test():
  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
[3,]   31   32   33
  D = einsum ( 'ii ->', A ):
[1] 66
  matrix_transpose_test():
  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
  AT = einsum ( 'ij -> ji', A ):
     [,1] [,2]
[1,]   11   21
[2,]   12   22
[3,]   13   23
  matrix_vector_multiplication_test():
  A:
     [,1] [,2] [,3]
[1,]   11   12   13
[2,]   21   22   23
  v:
[1] 1 2
  Av = einsum ( 'ij -> j', A, v ):
[1] 53 56 59
  vector_inner_product_test():
  u:
[1] 1 2 3
  v:
[1] 4 5 6
  w = einsum ( "i,i ->", u, v )
[1] 32
  vector_norm_test():
  u:
[1] 1 2 3
s = sqrt ( einsum ( "i,i ->", u, u ) )
[1] 3.741657
  vector_outer_product_test():
  u:
[1] 1 2 3
  v:
[1] 4 5 6
w = einsum ( "i,j ->", u, v )
     [,1] [,2] [,3]
[1,]    4    5    6
[2,]    8   10   12
[3,]   12   15   18










einsum_test():
  Normal end of execution.
Sun Aug  9 11:36:23 2026